Abstract

We present a phase field model suitable for studying phenomena, such as rafting, in which the elastic modulus mismatch (elasticinhomogeneity) plays a central role during microstructural evolution. This model requires a numerical technique for solving for the elastic stress fields in such inhomogeneous systems with, or without an applied stress. We present a technique, adapted from the literature on homogenisation, in which a periodic displacement field ($\mathbf{u}^{\star}$) and a homogeneous strain ($\mathbf {E}$) may be calculated consistent with a given macroscopic applied stress. We also describe an efficient Fourier transform based iterative technique for solving for $\mathbf {u}^{\star}$ and $\mathbf{E}$. We characterise this technique by comparing its results against known analytical results in a variety of settings.